Math Problem Statement

The null hypothesis should be rejected on the basis of the given P-value.

P−value=0.007, α=0.10, two-tailed test

True false question. True False

Solution

In hypothesis testing, the null hypothesis is rejected if the p-value is less than or equal to the significance level (α).

Here, the given p-value = 0.007 and α = 0.10 for a two-tailed test. Since 0.007 < 0.10, we reject the null hypothesis.

Thus, the correct answer is True.

Would you like an explanation on how the p-value relates to the hypothesis test, or more examples?

Here are some follow-up questions:

  1. How do you perform a hypothesis test in general?
  2. What are the differences between a one-tailed and two-tailed test?
  3. What is the significance level (α), and how is it chosen?
  4. What is the relationship between p-value and statistical significance?
  5. How would you interpret a p-value of 0.15?

Tip: Remember that a smaller p-value (typically less than 0.05) indicates stronger evidence against the null hypothesis.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
P-value
Significance Level
Two-Tailed Test

Formulas

P-value < α (Reject null hypothesis)

Theorems

Hypothesis Testing Theory

Suitable Grade Level

Grades 11-12